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Tpy6a [65]
3 years ago
7

What is the result when x^3-5x^2-18 is divided by x+3?

Mathematics
1 answer:
Masja [62]3 years ago
7 0
X3+5x2-18

Final result :

(x2 + 2x - 6) • (x + 3)
Step by step solution :

Step 1 :

Equation at the end of step 1 :

((x3) + 5x2) - 18
Step 2 :

Polynomial Roots Calculator :

2.1 Find roots (zeroes) of : F(x) = x3+5x2-18
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 1 and the Trailing Constant is -18.

The factor(s) are:

of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,3 ,6 ,9 ,18

Let us test ....

P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -14.00
-2 1 -2.00 -6.00
-3 1 -3.00 0.00 x+3
-6 1 -6.00 -54.00
-9 1 -9.00 -342.00
-18 1 -18.00 -4230.00
1 1 1.00 -12.00
2 1 2.00 10.00
3 1 3.00 54.00
6 1 6.00 378.00
9 1 9.00 1116.00
18 1 18.00 7434.00

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that
x3+5x2-18
can be divided with x+3

Polynomial Long Division :

2.2 Polynomial Long Division
Dividing : x3+5x2-18
("Dividend")
By : x+3 ("Divisor")

dividend x3 + 5x2 - 18
- divisor * x2 x3 + 3x2
remainder 2x2 - 18
- divisor * 2x1 2x2 + 6x
remainder - 6x - 18
- divisor * -6x0 - 6x - 18
remainder 0
Quotient : x2+2x-6 Remainder: 0

Trying to factor by splitting the middle term

2.3 Factoring x2+2x-6

The first term is, x2 its coefficient is 1 .
The middle term is, +2x its coefficient is 2 .
The last term, "the constant", is -6

Step-1 : Multiply the coefficient of the first term by the constant 1 • -6 = -6

Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is 2 .

-6 + 1 = -5
-3 + 2 = -1
-2 + 3 = 1
-1 + 6 = 5

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

(x2 + 2x - 6) • (x + 3)
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ollegr [7]
  -x + 1/2 = x + 4 1/2
  +x           +x
         1/2 = 2x + 4 1/2
       -4 1/2       - 4 1/2
        -4 = 2x
         x = -2
6 0
3 years ago
Can someone please help me with this questions
Ludmilka [50]

Step-by-step explanation:

a. 3⁴

b. 7⁵

c. 10²

d. 5⁷

Hope this helps?

8 0
3 years ago
The mean of x y and z is 20. find the mean of x-5 y+4 z-5
Dafna11 [192]

Answer:

18

Step-by-step explanation:

Sum of x, y and z = 20 × 3

                             = 60

x-5+y+4+z-5 = 60-5+4-5

                    = 54

Mean of x-5, y+4 and z-5

= 54 ÷ 3

= 18

7 0
2 years ago
Could someone help me please ​
Alexxx [7]

1. 3x+9-9=18-9      

3x=9

x=3

2. 4x-12=20

4x-12+12=20+12

4x=32

x=8

3. x+0-0

x=0

4. x/2-2+2=9+2

x/2=11

(2)(x/2)=11(2)

x=22

5. 12x-21=3

12x-21+21=3+21

12x=24

x=2

6. 3x-15=18

3x-15+15=18+15

3x=33

x=11

7. 3x-25=14

3x-25+25=14+25

x=13

8. 3x+16=22

3x+16-16=22-16

x=2

9. 2x-8=2

2x-8+8=2+8

2x=10

x=5

10. 9x-18=9

9x-18+18=9+18

9x=27

x=3

11. x+0=0

x=0

12. 9x-8=19

9x-8+8=19+8

9x=27

x=3

If  you want to check my answers

use substitution method by using the x into for each equation.

7 0
3 years ago
Read 2 more answers
15 points!
Phantasy [73]

Hi there! You are provided with two points, this is all you need to calculate the line's slope.


The equation for slope is:

\frac{y2 - y1}{x2 - x1}

\frac{10 - 8}{3 - 7} = -\frac{2}{4}

Slope: -2/4


Point slope form, or y-y1 = m(x - x1). All we have to do is take the x and y coordinates of either point, as well as the slope, and plug them into the equation.

y - 10 = -2/4(x - 3)


Write the equation in slope-intercept form (y=mx+b)

y - 10 = -2/4(x-3)\\y = -2/4(x-3) + 10\\y = -2/4x + 1.5 + 10\\y = -2/4x + 11.5


A) -2/4

B) y - 10 = -2/4(x - 3)

C) y = -2/4x + 11.5

8 0
3 years ago
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